Bosonic Ghosts at c = 2 as a Logarithmic CFT

Abstract

Motivated by Wakimoto free field realisations, the bosonic ghost system of central charge c = 2 is studied using a recently proposed formalism for logarithmic conformal field theories. This formalism addresses the modular properties of the theory with the aim being to determine the (Grothendieck) fusion coefficients from a variant of the Verlinde formula. The key insight, in the case of bosonic ghosts, is to introduce a family of parabolic Verma modules which dominate the spectrum of the theory. The results include S-transformation formulae for characters, non-negative integer Verlinde coefficients, and a family of modular invariant partition functions. The logarithmic nature of the corresponding ghost theories is explicitly verified using the Nahm–Gaberdiel–Kausch fusion algorithm.

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Ridout, D., Wood, S. Bosonic Ghosts at c = 2 as a Logarithmic CFT. Lett Math Phys 105, 279–307 (2015). https://doi.org/10.1007/s11005-014-0740-z

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Mathematics Subject Classification

  • 17B68
  • 17B69

Keywords

  • Logarithmic conformal field theory
  • vertex algebras
  • modular transformations
  • fusion